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Key ideas
Key ideas
The derivative may be represented physically as a rate of change and geometrically as the gradient or slope function.
Examining rates of change close to turning points helps to identify intervals where the function increases/decreases, and identify the concavity of the function.
I can differentiate a variety of functions including sums and multiples of functions.
I can explain how to use the chain rule for composite functions.
can explain how to use the product and quotient rules.
The Power rule
The Power rule
https://www.youtube.com/watch?v=TgIl15Nlg_U
MIT grad shows how to find the derivative using the Power Rule, one of the derivative rules in calculus. It is a shortcut for taking derivatives of polynomial functions with powers of x. To skip ahead:
1) For HOW and WHEN to use the power rule, skip to time 0:22.
2) For how to use the power rule when you have a FRACTIONAL or NEGATIVE POWER, skip to 5:22
Derivatives of basic functions
Derivatives of basic functions
This must be one of the first videos PatrickJMT ever made:
Rules of differentiation
Rules of differentiation
Composite functions
The product of two functions
The quotient of two functions
Product rule, Quotient rule and Chain rule
Product rule, Quotient rule and Chain rule
Theory: The chain rule
Theory: The chain rule
The Chain rule is used where a function can be regarded as a composite of two other functions: g(f(x)). We choose f(x) to be u and differentiate with respect to u (dy/du). Then we differentiate u with respect to x (du/dx). Together they make dy/dx.
This often comes down to:
Theory: The product rule
Theory: The product rule
When we can identify a function to consist of two functions being multiplied, the derivative can be found by using the product rule.
Theory: The quotient rule
Theory: The quotient rule
When we can identify a function to consist of two functions being divided, the derivative can be found by using the quotient rule.
Pop-Quiz A
Pop-Quiz A
Pop Quiz B
Pop Quiz B
The derivative of ex and Sin (x)
The derivative of ex and Sin (x)
Derivatives of Trigonometric functions
Derivatives of Trigonometric functions
The derivative of a*sin(bx)
The Derivative of e^x
The Derivative of e^x
https://www.geogebra.org/material/show/id/dt49ugch
The derivative of Sin(x)
The derivative of Sin(x)
AHL5.15 Derivatives of inverse trigonometric functions
AHL5.15 Derivatives of inverse trigonometric functions
These are the derivatives of arcsin (x), arccos(x) and arctan(x). Remember that you may need to use the product, quotient and/or chain rule with these as well.
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